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Simplifying 450x2 + 180x3 + -10x4 = 0 Solving 450x2 + 180x3 + -10x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10x2'. 10x2(45 + 18x + -1x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(45 + 18x + -1x2)' equal to zero and attempt to solve: Simplifying 45 + 18x + -1x2 = 0 Solving 45 + 18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -45 + -18x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + -18x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -18x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -18x + x2 = 0 + 45 -18x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -18x + x2 = 45 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 45 + 81 Reorder the terms: 81 + -18x + x2 = 45 + 81 Combine like terms: 45 + 81 = 126 81 + -18x + x2 = 126 Factor a perfect square on the left side: (x + -9)(x + -9) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (x + -9) equal to 11.22497216 and -11.22497216.Subproblem 1
x + -9 = 11.22497216 Simplifying x + -9 = 11.22497216 Reorder the terms: -9 + x = 11.22497216 Solving -9 + x = 11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 11.22497216 + 9 Combine like terms: -9 + 9 = 0 0 + x = 11.22497216 + 9 x = 11.22497216 + 9 Combine like terms: 11.22497216 + 9 = 20.22497216 x = 20.22497216 Simplifying x = 20.22497216Subproblem 2
x + -9 = -11.22497216 Simplifying x + -9 = -11.22497216 Reorder the terms: -9 + x = -11.22497216 Solving -9 + x = -11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -11.22497216 + 9 Combine like terms: -9 + 9 = 0 0 + x = -11.22497216 + 9 x = -11.22497216 + 9 Combine like terms: -11.22497216 + 9 = -2.22497216 x = -2.22497216 Simplifying x = -2.22497216Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.22497216, -2.22497216}Solution
x = {0, 20.22497216, -2.22497216}
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